High intensity discharge lamps have been now utilized as automobile's head lamp and a projector lamp. Because of the nature of this application, the lamps have to increase luminous flux rapidly upon being turned on. Particularly, the automobile's lamps have to satisfy a requirement of increasing the luminous flux to a sufficiently high level within a few seconds. When designing the ballast that ensures a rapid increase of the luminous flux, it should be taken into consideration that a possible variation in lamp characteristic may bring about an appreciable delay in reaching a prescribed light output level due to overshooting or undershooting of the light output.
Japanese Patent Publication No. 2946384 discloses a ballast that is intended to compensate for the lamp characteristic variation in an attempt to increase the light output to a sufficiently high level without a delay. The ballast monitors the voltage being applied to the lamp and controls the output power in accordance with a specific change in the monitored voltage. The output power, which is corrected by the monitored voltage, is set by an analog circuit to vary with respect to time from a large wattage starting condition to a steady-state constant wattage condition. However, the prior ballast is found not to be sufficiently satisfactory for correcting the output power in exact reflectance of the monitored condition of the lamp, because of that the output power is caused to vary only with some delay due to a time constant inherent to the analog circuit, and therefore not in an exact match with the lamp characteristic given in a transition period from the lamp starting condition to the steady-state condition, and also because of that the target output power to be subsequently given is only determined based upon the current output power and not from the expected output power at the subsequent time.